Archive for category Meta-Philosophy
I am better understanding the “dark night of the soul” that mathematics has been for me.
I think that truth needs to involve an element of fantasy. That sounds like a paradox; but I think that our fantasies are true.
If I visualize something so vividly that it feels at least as real to me as physical reality, what grounds do I say that physical reality is real, and the visualization is unreal?
Well, one ground would be that other people can’t see the visualization; but I’ll address that issue later.
Try it. Visualize a red triangle. Visualize it so strongly that it becomes as real as your own hand. Then visualize it so strongly that it’s more real than your hand. It can be done.
People regularly achieve this sort of transcendence of physical reality on the wings of pure faith. Think of the ascetics who deprive and punish their bodies for the sake of a belief. Think of the feminists, who have managed to make widely accepted a truth that has no evidence other than what people’s hearts tell them. Think of the mathematicians, who study a vast paradise of nonexistent and impossible objects. Think of the fiction writers, who live in an imaginary world of their own creation.
Fantasy, the truth that comes from inside us, is subjective truth. The truth that comes from examining the outside world, is objective truth.
Subjective truth is considered by many to be nonexistent. And indeed, I cannot assert the existence of subjective truth in the same way that I can assert that 2+2=4. The reason is that subjective truth is subjectively true; whereas objective truth is objectively true. But subjective truth is not objectively true. Similarly, objective truth is not subjectively true.
Objective truth can only be determined through the methods of empiricism. For subjective truth, the method is this: whatever you wish to be true, is true.
The nature of our experience at this nexus places great emphasis on objective truth. We are, in the ordinary course of things, absorbed in the shuffle of the physical world and its necessities. And this same emphasis on objectivity is reflected in our intellectual climate.
Subjective truth is hard to find, hard to notice, hard to hold onto. But it is better and more important than objective truth.
People have different subjective truths. I can see my own visualizations; you cannot. My passions are not your passions. My ideals are not your ideals.
There is therefore great paradox in trying to share one’s subjective truth. Subjective truth is not objectively true. What is true for me, may not be true for you. For the most part, therefore, we must have our own truth and let others have theirs. The problem of sharing truths is a hard one.
I cannot wish to share my truth with another, if for them it is falsehood. I can only wish to share it with them, if for them it is truth.
Mathematical logic can basically be characterized as the search for an epistemology. We want to design some formal system which lets us prove all true facts: so then we can decide what to believe just based on what the formal system says. And of course the system needs to prove itself to be correct; because otherwise, how would we know that the system is correct?
That’s the basic, obvious, naive hope of mathematical logic. Basically, we want an epistemology: a formal, mathematically rigorous epistemology that can prove all true facts, including the true fact that it is the correct epistemology.
Now there’s already some magical thinking inherent in this idea. How do we know the epistemology is correct? Why, because the epistemology says so!
So that’s a circular argument; but what’s the alternative? How could we possibly know that our epistemology was correct, other than by using our epistemology?
There’s that problem, and it shows up even before Gödel’s theorem. But then Gödel’s theorem tells us that self-validating epistemologies aren’t even logically possible. It’s not just that if you make a self-validating epistemology, its proof of its own correctness doesn’t mean anything because it’s a circular argument. No, it’s worse: no coherent epistemology even contains a proof of its own coherence.
And we’re not even talking about the epistemology proving itself to be true. No, we’re talking about a much weaker condition: the epistemology proving itself to be consistent, i.e., not contradicting itself. An epistemology can’t even prove itself consistent — at least not if it really is consistent.
Oh, and then things get even worse. Along comes my inconsistency theorem, which says that all of our existing epistemologies do in fact contradict themselves. Damn!
So then we try to come up with an epistemology that doesn’t contradict itself. I came up with one recently. At any rate, my inconsistency theorem doesn’t work in this epistemology; and I can argue pretty forcefully that it is consistent.
Basically, the reason I can say that is this. In this theory, whether or not a statement is true is determined by the outcome of a certain computer algorithm. The computer algorithm always halts, and always outputs exactly one of true or false, no matter what statement you put in. So unless the world magically splits in two and the computer program says both yes and no, despite being programmed to say only one of those, the theory is clearly consistent.
But how do we prove it to be consistent? In math we don’t accept those sorts of vague verbal arguments, especially not for something as important as the internal coherence of the very foundation of our belief system. We want a formal proof, not a verbal argument.
Well, interestingly, Gödel’s theorem still applies to this theory, and it can’t prove itself consistent. But even if it could, what would that mean?
Logic is absolutely filled with consistency proofs. Take any well-known formal system, and you can find half a dozen different consistency proofs for it. But not only are all such consistency proofs circular and therefore meaningless — they’re wrong! Every well-known formal system is inconsistent. We can still prove them consistent in half a dozen different ways.
I hope that demonstrates the utter futility and fatuity of consistency proofs. We can prove any system to be consistent — whether or not it actually is! We can prove any system, consistent or inconsistent, to be consistent. Given that fact, proving that a system is consistent basically forms no argument for it actually being consistent.
So let’s return to the beginning. We want to adhere to an epistemology. But we need to justify that our epistemology is correct. If we do that using our epistemology, then we’re arguing in a circle. If we do that by stepping outside our epistemology, then we’ve just violated our epistemology. (Every epistemology is a dictum of the form, “thou shalt believe all and only the things determined by these rules.”) But then things get worse because we provably can’t construct a self-validating epistemology, most of our epistemologies contradict themselves, and every argument to the effect that any epistemology is coherent is demonstrably meaningless.
Long story short, skepticism wins. We can’t achieve an ironclad belief system, where everything is justified to the point of absolute certainty. It’s just obvious that we can’t do that with anything empirical; but now formal reasoning has taught us that we can’t even do it in the rarefied realm of pure math.
When you penetrate to the very heart of reason, when you gaze upon its hidden starry essence, you find not a perfect and indestructible core of truth, but a bug in the Matrix, a crack in the wall, a strange sort of Zen joke about epistemology. And you go home having learned that you can’t know anything for certain.
The academician does not see the truth.
He does not open his ears to the warbling sound of his inner teacher,
who speaks of the brightest of noons and the darkest of sunsets,
the highest of foothills and the lowest of mountains.
He does not set his gaze on the soft, caressing glow of truth,
but fades out that glorious sunset
with his Kodak monochrome image capturing software,
the tool of those great census bureau workers of the universe, reason.
The academician speaks the truth about all things outside,
but he omits the truth about himself,
and in this omission all of his words are reduced to so much dust,
so many files and records of tiny bits of data.
In his quest to know everything he finally knew nothing,
and in this miserable not-knowing he might finally learn to hear himself.
Let us hope!
Earlier tonight I was walking back from a meditation session, and I concluded that math was nothing but a giant power trip, something people use to control other people and the natural world. So in my mind I renounced math, with that little nagging voice saying that there was no way I was done with it.
Later this evening I found myself reading about sheaves, and ejaculating wild screams of ecstasy as if I were a woman in orgasm. What a deep conundrum this is! What other human could possibly empathize with my soul’s dilemma?
Most of the time, we don’t have the option of formally proving our ideas. It’s really only in math and science that we can do this. But most intellectual problems in the real world don’t fit that paradigm. Most real-world intellectual problems are decision problems. You have a group of people who are trying to decide something (a workplace, a family, a country, a group of friends, a romantic partnership). They need to share ideas with each other, and eventually they need to agree on something. But they need to do this without the use of formal proof, because almost always, you can’t prove that your idea for what to do is the best one.
The situation is the same in philosophy and religion. We don’t have the luxury of formal proof in these disciplines, but we still need to think about things together and eventually agree about something.
We want to hold philosophical and religious beliefs, but it’s sort of meaningless to do so unless other people agree with us. I’ve tried being a lone believer who has his own perspective on reality that nobody else shares. But I can’t shake this feeling that I’ve regressed into solipsism when I do that. If my beliefs are unproven and held only by me, by what metric are they tested? How do I know that they’re right? How could I possibly distinguish between a private true belief, and a private delusion?
“Proof” can take many forms. There’s formal proof, which is the best kind. But you can also know something just through having experienced it. It is in this sense which I know, for instance, that my happiness is mostly a function of my inner state, rather than a function of what’s going on in my life. I’ve ascertained that experientially, though I can’t prove it to somebody else.
And a further kind of proof, I think, comes from a lot of people adopting a belief. We’ve never had any formal proof that democracy is a good idea; but the fact that a lot of people believe in it constitutes a strong argument for it. Similarly, the very fact that most people believe in God constitutes an argument in favor of God’s existence.
Now, if I have an idea, and I share it with other people, two things can happen. Other people can think the idea is good and adopt it; which boosts my confidence that the idea is right. Or other people can say, “hmm, I don’t think that’s such a good idea;” which lowers my confidence that the idea is right.
People act as a sounding board for each other’s ideas. You put an idea out there, and if it echoes throughout the social matrix, resounding again and again, then it’s a good idea. If it dies soon after it leaves its maker, then it’s not a good idea; so the theory goes.
The problem is that our social matrix doesn’t seem to be a very efficient sounding board. I’ve probably written up hundreds of philosophical ideas, but the number of these ideas that gained traction among my peers is close to zero. I spent years making music, but nobody really listened to my music.
Am I to conclude, from these facts, that I’m a bad philosopher and a bad musician? That seems false. More like, people aren’t listening to me. But I can’t just blame other people: maybe I’m not listening to other people either. We’re not listening to each other.
I think this is what stymies philosophy and metaphysics. To do philosophy, you really need the sounding board effect, because it’s basically all you’ve got. The social sounding board needs to be sensitive and of high quality. People need to be able to give you honest and sympathetic feedback based on genuine listening to your idea.
We don’t have that for philosophy. Even philosophy departments aren’t that. If you tell your idea to a philosophy professor, they’ll probably say it’s wrong. Everybody thinks everybody else is wrong in philosophy departments. That doesn’t get you anywhere; being told you’re always wrong teaches you nothing.
I think science has flourished over philosophy, religion, art, music, etc., in large part because science has the advantage of formal proof. With science, you can have ideas getting widespread traction, without people, y’know, actually having to listen deeply and sympathetically to each other. We don’t know how to listen, so we like science.
Meet Warren. Warren is a physicist. He loves understanding things. He gets excited about calculus. He thinks that black holes are the coolest things ever. He thinks that they’re even cooler once you know the physics. To Warren, a rainbow doesn’t lose any of its beauty after you understand how it works. What Warren wants to do with his life is use science to make the world better, and share his love for the truth with other people.
Now meet Alexander. Alexander is a lot like Warren. He, too, loves understanding things. He, too, loves the truth. But unlike Warren, Alexander believes in God. He had a conversion experience as a teenager, where God revealed Himself to him, and his life was changed forever. Now Alexander studies philosophy, theology, metaphysics. He sees himself as a privileged witness to a great, hidden truth. He sees himself as a light-bringer, one who was sent to bring knowledge of the spirit to the world.
Now meet Ram. Ram is a lot like Alexander. He, too, has experienced enlightenment. He, too, feels himself to have been a witness to a deep, eternal truth. But Ram rarely talks about it. Maybe he’s a monk living in the forest; maybe he’s homeless; maybe he’s bagging groceries at the store near your house; maybe he’s teaching math at a local high school. Ram is enlightened, but his response to that fact was just to keep living his life. He’s the Zen master on the corner; he’s the Buddha begging for change; he is an enlightened man disguised as an ordinary person.
Warren is the rationalist. Alexander is the metaphysician. Ram is the mystic. These three have an intimate, tangled relationship with each other. I have seen the archetypal conflicts of that relationship played out in my life over and over again: between me and my friends, between public figures and other public figures, and most especially, between me and myself.
I pointed out that Alexander is a lot like Ram. But Warren is a little like Ram, too. Warren’s wonder at the beauty and order of the universe can approach the same sort of stupefying ecstasy whose momentary occurrence shapes and defines the lives of Ram and Alexander. Warren’s steadfast conviction of the worth of knowing, the vow he made in his heart to follow the truth wherever it leads, is rather akin to the religious conviction that captivates and consumes Ram and Alexander.
Warren has strong beliefs about reality. He believes that science is the only way to seek the truth. He believes that materialism is true; reductionism is true; the mind is the brain; God does not exist; we do not have souls; everything follows the laws of physics. To Warren all of these things are basic and obvious.
Alexander, too, has strong beliefs about reality. He believes that God is real, and the purpose of human life is to seek union with Him. Alexander believes that we live forever. He believes in a metaphysical realm beyond the physical universe and the means of human observation. Unlike Warren, who believes that truth comes only through reasoning and empirical observation, Alexander believes that truth can come through gnosis, through “inner knowing.”
Warren and Alexander have an ongoing drama. They each have their philosophical convictions, and each feels that these are important points that everybody needs to appreciate. Each feels not only that their beliefs are *true*, but that the world would be a better place if everybody accepted them. But they don’t agree with each other, and so they get into interminable arguments.
What a complex relationship these two have! How many layers there are to their social dynamic! Each feels superior to the other. Each feels like he is enlightened one, and the other is lost and off the path. Each wants to convince the other.
Why? Partly as a demonstration of dominance. Partly out of a sincere desire to help the other, by sharing with the other what was so valuable to the self. And partly out of a sense of insecurity, a buried fear that maybe you are right and I am wrong.
And funnily enough, each feels, deep down, that the other has something to offer them. They might never admit it. But this is part of the perversity of their relationship, that each is rather attracted to the other’s philosophy. If only subconsciously, they want to learn it.
If you are skeptical of this claim, consider this. When I am totally sure that somebody else is wrong, and I don’t expect to change their minds, then I just ignore them. To feel the impulse to argue, I need a little fear. Cranks don’t scare me. What scares me is when I think somebody’s wrong, but I have the feeling of truth pulling me toward their view, and yet I can’t stand the thought that it really is true. That is when I will start trying to refute them.
Warren is scared of Alexander, and Alexander is scared of Warren. Neither will admit it. Warren admires Alexander, and Alexander admires Warren. Neither will admit it. This is the secret, buried aspect of their relationship. Neither will admit that the other affects them.
That is the social aspect of Warren and Alexander’s relationship. But they see their problem as an intellectual one. For them, it is not a matter of how you make me feel and how I make you feel. Rather, it is a question of whether or not God really exists, whether or not the mind really is the brain, and so forth. It is purely a question of what is really true, and not about the people talking about it. That is how they feel.
To a great extent, they obscure their social problems from themselves by thinking that there is only an intellectual problem. Of course, let us not make the opposite mistake, of thinking that there is only a social problem, and ignoring the intellectual problem. It is clear that there is a genuine intellectual problem being discussed. But this intellectual aspect is almost overly clear; it is so naked and so thoroughly examined that it seems like there is almost nothing more to gain from analyzing it further. On the other hand the social aspect of the problem is quite obscured, quite ignored, quite neglected. Mightn’t making new intellectual progress depend upon first making new social progress? Mightn’t having a productive discussion depend upon finding a new *way* of discussing?
So that is Warren and Alexander. There is another complex relationship that we must examine: that between Alexander and Ram.
Ram is quite obviously the entire source of Alexander’s inspiration. Alexander can be himself only insofar as he can approximate being like Ram. His metaphysical knowledge is an empty and worthless shell indeed without the pure, experiential mysticism that Ram lives so fully; and Alexander *knows* this, if not in every moment.
Alexander’s entire game can be described like this. Having imperfectly grasped, through the veil of the intellect, the wisdom that Ram lives, Alexander practices a mysticism that is always distorted by his continual attempts to employ logic in areas where it is not helpful. (The concept of “areas where logic is not helpful” amuses Warren immensely!) Sometimes Alexander is oblivious to his own folly; other times he is aware of it but doesn’t know what to do about it. He doesn’t know *how* he would live other than through his intellect.
Ram’s attitude towards Alexander is very simple. For Ram, Alexander is exactly as beautiful and insignificant as the flowers he passes on his morning walk. But Alexander has a very complex attitude towards Ram. He is allured, bewildered, mystified, humbled, belitted by Ram. And, at the same time, he routinely utterly fails to notice when Ram passes him by on the street. He routinely fails to hear Ram’s worldless teachings because he drowns them out by all his talking.
That is Ram and Alexander. Our final pairing is Warren and Ram, who barely know each other at all. Warren doesn’t know what mysticism is, and even if he did, he would have no problem with it. Warren doesn’t have anywhere to disagree with Ram, because Ram never says anything. On the other hand, Ram has heard of science, and he finds it as beautiful and insignificant as the flowers he passes on his morning walk.
A corrollary of this fact is that, for Ram, there is no problem of reconciling rationality and mysticism. Ram never saw any conflict to begin with.
Why don’t we understand psychology? We have highly developed knowledge of almost everything we can observe, other than people. The light of science has been shone into every corner of the observable world, but for some reason it has not penetrated the realm of the mind to any significant extent. Why not?
A lack of curiosity is not the reason. There is little we are more curious about than ourselves.
Maybe the reason is that introspection is hard. We have high-fidelity sense organs to tell us about the outside world. Though we can see our own thoughts, we cannot see them with the kind of clarity that we can see the outside world. Our thoughts are shadowy and fleeting unto us.
And yet, we have very solid knowledge of the subatomic world, despite the most paltry means of observing it. Our introspective powers, even if they are dim, should be enough for a determined investigator to make progress.
Recognizing that introspection hasn’t gotten us to a general theory of psychology, psychology has now turned towards behavioral and neuroscientific methods. But these don’t seem to be working either. We still don’t have anything even remotely resembling a general theory of psychology. The question remains, why?
I think the reason is that people are complicated. The chains of causality which go into a “simple” human behavior are infathomably massive. They resist analysis.
With the most paltry means of observation, physicists were able to figure out the rules governing subatomic particles, because the rules governing subatomic particles are fundamentally simple. We haven’t been able to do the same with people, because the rules governing people are fundamentally complicated. Maybe an approximately correct theory of psychology would involve terabytes of equations.
How does one approach such a problem? My final answer is, I don’t know. I don’t have much experience with solving impossibly difficult problems.
I do think that I know some things about how to study psychology. In particular, I think I know that experimental psychology is not the best way to make progress on this problem.
Psychology, like many other fields, suffers from “science envy.” It wants to be like the physical sciences. But it shoots itself in the foot by trying to do this. What works for studying atoms, molecules, etc., doesn’t work for studying the mind.
In the physical sciences, the problem is one of studying fairly simple phenomena to the point of exhausting everything there is to know about them, and formulating fully precise and general theories of how they work. The methods of physical science work well for doing this.
In psychology, the problem is one of trying to learn more about an almost intractably complicated phenomenon. The nature of the task is that fully precise and general theories are basically out of the question. Our knowledge will always be vague and tentative, and full of exceptions. And, because we are studying people, our knowledge will always be influenced by our own biases.
In academia there are strong norms against saying things that are vague, things that are tentative, things that have exceptions, and things that are biased. I think that these norms are not helpful for psychology. In psychology, when we refuse to say things that aren’t perfect, we end up saying nothing interesting.
How does one treat an intractably difficult problem? Not by waiting until one’s thoughts are perfect before sharing them. Not by holding others’ thoughts to high standards of correctness. Not by trying prematurely to fit the data into a generalized and rigid framework. Rather, one floats all kinds of hypotheses, without taking any hypothesis too seriously, and remaining radically open-minded.
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